Ex 6.2, 4 - Find intervals f(x) = 2x2 - 3x is (a) increasing - Find intervals of increasing/decreasing

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  1. Chapter 6 Class 12 Application of Derivatives
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Ex 6.2,4 Find the intervals in which the function f given by f (𝑥) = 2𝑥2 – 3𝑥 is (a) strictly increasing (b) strictly decreasing f (𝑥) = 2𝑥2 –3𝑥 Step 1: Calculating f’(𝑥) ﷐𝑓﷮′﷯﷐𝑥﷯ = 4𝑥 – 3 Step 2: Putting f’ (𝑥) = 0 4𝑥 – 3 = 0 4𝑥 = 3 𝑥 = ﷐3﷮4﷯ Step 3: Drawing graph Point 𝑥 = ﷐3﷮4﷯ divide the real line into 2 disjoint intervals i.e. ﷐–𕔴 , ﷐3﷮4﷯﷯ & (﷐3﷮4﷯ ,𕔴 ) Step 4: Hence ﷐𝑎﷯ f is strictly increasing in ﷐﷐𝟑﷮𝟒﷯ , 𕔴uc1﷯ ﷐𝑏﷯ f is strictly decreasing in ﷐−𕔴﷐𝟑﷮𝟒﷯﷯

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